Evaluating atmospheric CO2 inversions at multiple scalesover a highly inventoried agricultural landscapeANDREW E . SCHUH* † , THOMAS LAUVAUX ‡ , TR I S TRAM O . WEST § , A . SCOTT

DENNING ¶ , K ENNETH J . DAV I S ‡ , NATASHA MILES ‡ , S COTT R ICHARDSON ‡ , MAREK

UL IASZ ¶ , E RANDATH IE LOKUP IT I YA k, DAN IEL COOLEY * * , ARLYN ANDREWS † † and

STEPHEN OGLE†

*Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, CO, USA, †Natural Resources

Ecology Laboratory, Colorado State University, Fort Collins, CO, USA, ‡Department of Meteorology, Pennsylvania State

University, University Park, PA, USA, §Joint Global Change Research Institute, Pacific Northwest National Laboratory, College

Park, MD, USA, ¶Department of Atmospheric Sciences, Colorado State University, Fort Collins, CO, USA, kDepartment of

Zoology, University of Colombo, Colombo 03, Sri Lanka, **Department of Statistics, Colorado State University, Fort Collins,

CO, USA, ††NOAA Earth System Research Laboratory, Boulder, CO, USA

Abstract

An intensive regional research campaign was conducted by the North American Carbon Program (NACP) in 2007

to study the carbon cycle of the highly productive agricultural regions of the Midwestern United States. Forty-five

different associated projects were conducted across five US agencies over the course of nearly a decade involving

hundreds of researchers. One of the primary objectives of the intensive campaign was to investigate the ability of

atmospheric inversion techniques to use highly calibrated CO2 mixing ratio data to estimate CO2 flux over the

major croplands of the United States by comparing the results to an inventory of CO2 fluxes. Statistics from

densely monitored crop production, consisting primarily of corn and soybeans, provided the backbone of a well

studied bottom-up inventory flux estimate that was used to evaluate the atmospheric inversion results. Estimates

were compared to the inventory from three different inversion systems, representing spatial scales varying from

high resolution mesoscale (PSU), to continental (CSU) and global (CarbonTracker), coupled to different transport

models and optimization techniques. The inversion-based mean CO2-C sink estimates were generally slightly

larger, 8–20% for PSU, 10–20% for CSU, and 21% for CarbonTracker, but statistically indistinguishable, from the

inventory estimate of 135 TgC. While the comparisons show that the MCI region-wide C sink is robust across

inversion system and spatial scale, only the continental and mesoscale inversions were able to reproduce the

spatial patterns within the region. In general, the results demonstrate that inversions can recover CO2 fluxes at

sub-regional scales with a relatively high density of CO2 observations and adequate information on atmospheric

transport in the region.

Keywords: agriculture, atmospheric inversions, carbon cycle, CO2 emissions, inventory, Mid-Continent Intensive

Received 6 November 2012; revised version received 6 November 2012 and accepted 10 December 2012

Introduction

For over half a century, the analysis of trace gases in

the atmosphere has been a rich source of information

about the contemporary global carbon cycle. Early

studies of the secular trend and seasonal cycles of CO2

mixing ratio revealed the accumulation of fossil carbon

and the striking role of terrestrial ecosystems in plane-

tary metabolism, and by the mid-1960s scientists had

used spatial patterns in CO2 and its isotopic composi-

tion to establish rates of atmospheric mixing (Bolin &

Erickson, 1959; Bolin & Keeling, 1963), the penetration

of anthropogenic CO2 into the oceans, and the existence

of a net sink in the terrestrial biosphere (Bolin &

Keeling, 1963). Beginning in the 1980s, the global

network of sampling stations from which accurate CO2

measurements were available expanded rapidly with

CO2 measurements to support carbon cycle research.

Denser data allowed formal estimation of the spatial

patterns of sources and sinks at continental and ocean

basin scale using inverse modeling, which also required

quantitative accounting for atmospheric transport

(Pearman & Hyson, 1981; Heimann & Keeling, 1986;

Fung et al., 1987; Tans et al., 1990). A community of

global CO2 inverse modelers emerged during the 1990s

and performed a series of atmospheric transport

intercomparison (TransCom) experiments. TransComCorrespondence: Andrew E. Schuh, tel. + 970 491 8362, fax + 970

491 8449, e-mail: aschuh@atmos.colostate.edu

1424 © 2013 Blackwell Publishing Ltd

Global Change Biology (2013) 19, 1424–1439, doi: 10.1111/gcb.12141

documented the sensitivity of estimated source/sink

patterns to differences in advection, turbulence, and

cloud transport among atmospheric models (Law &

Simmonds, 1996; Denning et al., 1999; Gurney et al.,

2002; Baker et al., 2006).

Despite decades of measurements, modeling, and

field experiments, interactions between the carbon

cycle, climate, and management now constitute a lead-

ing source of uncertainty in projections of 21st century

climate change. Experiments with fully coupled carbon

cycle-climate models show a range of over 250 ppm in

CO2 by 2100 given identical fossil fuel emissions (Frie-

dlingstein et al., 2006; Solomon et al., 2007). Estimation

of space/time variations of carbon sources and sinks by

transport inversion provide an important constraint on

coupled Earth system prediction. Tracking interannual

variations in carbon source and sinks using transport

inversion of atmospheric observation has become

nearly routine in the 21st century (Peters et al., 2007,

2010). However, the relatively sparse data still require

aggressive regularization through the use of Bayesian

priors (Baker et al., 2006), geospatial smoothing (Michalak

et al., 2004), or pre-aggregation of sources and sinks into

coarse basis functions within which space/time patterns

of flux are assumed to be known (Peters et al., 2007).

Formal evaluation of the accuracy of regional sources

and sinks has remained elusive due to a lack of reliable

independent measurements of regional CO2 fluxes.

CO2 fluxes can be estimated locally by eddy covariance

(Baldocchi et al., 2012), but the area represented by

these estimates is generally a few square kilometers at

maximum, far smaller than can be estimated from

available concentration data. Field experiments during

which greatly enhanced data collection is performed

temporarily over a limited region and time period has

provided opportunities to evaluate transport inversions

(RECAB: Filippi et al., 2003; ChEAS: http://cheas.p-

su.edu/Chen et al., 2008; LBA: http://daac.ornl.gov/

LBA/lba.shtml, COBRA: Gerbig et al., 2003; CERES:

Dolman et al., 2006; ORCA: Goeckede et al., 2010a;

ACME-07: Desai et al., 2011). Even for such limited

regions, local bottom-up flux products (estimated from

surface data, in contrast to models) must be interpo-

lated across orders of magnitude of spatial scales to

provide a quantitative constraint on top-down fluxes

(estimated from atmosphere measurements).

As part of the North American Carbon Program

(NACP) (Wofsy & Harriss, 2002; Denning, 2005), the

Mid-Continent Intensive (MCI) field experiment was

designed to evaluate innovative methods for CO2 flux

inversion and data assimilation by performing quanti-

tative comparison of top-down and bottom-up inven-

tory estimates of a regional carbon budget. The

experiment was performed over a relatively flat,

heavily managed landscape in the mid-continent region

of North America and featured a high density of atmo-

spheric CO2 measurements (Ogle et al., 2006). A signifi-

cant advantage of the study region was the fact that

this area was relatively flat and devoid of complex

topography, that would have made the meteorology

more difficult to model for the inversions. Atmospheric

CO2 concentrations were measured using in situ analyz-

ers installed on a ring of communication towers in the

region (Miles et al., 2012), and vertical profiles of CO2

were measured by a short dense aircraft sampling cam-

paign (Martins et al., 2009). Another key advantage of

this region for the inventory compilation was the

detailed statistics available from US Department of

Agriculture on commodity production in this economi-

cally important region. Consequently, the bottom-up

inventory was developed at a high spatial resolution

compared to previous studies and provided highly

resolved maps of the annual uptake and release of CO2

by agriculture, forests, fossil fuel combustion, and

human respiration (West et al., 2011). In addition, sur-

face fluxes over croplands were also estimated by eddy

covariance (Meyers & Hollinger, 2004; Verma et al.,

2005) and used to evaluate bottom-up inventory

methods and as observational data for crop phenology

models (Lokupitiya et al., 2009) used by the inversions.

Our primary objective in this study was to compare

two sets of regional inversion estimates for the MCI

region to a bottom-up inventory of fluxes. Estimates

from a third inversion were also included, CarbonTrac-

ker (CT), which is a global scale inversion that does not

use the finer scale network of observations in the MCI

region. This inversion served as a standard for compar-

ison to evaluate the influence of the higher density

network on the inversion results, and we anticipated

that the regional inversions would provide a more

accurate estimation of CO2 flux in the MCI study. Our

secondary objectives were to explore reasons for differ-

ences between the inversion at both regional and sub-

regional scales, with a primary focus on atmospheric

transport, boundary inflow of CO2, and a priori CO2

flux estimates. This research extends work of Lauvaux

et al. (2012a,b), incorporates CO2 flux estimates from

the operational CT system (Peters et al., 2007), and

presents new results for the MCI following the method-

ology of Schuh et al. (2010). The three inverse analyses

presented span a range of spatial domains from global

to regional, and also a range of resolutions and differ-

ent techniques for regularization. Comparing their

results allows us to explore, for the first time, the

strengths and weaknesses of many methodological

choices in regional carbon analysis for an intensive

campaign (MCI) in which we have uniquely detailed

independent data from the bottom-up inventory.

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

PREDICTING CO2 FLUX OVER THE MIDWESTERN USA 1425

Materials and methods

Observational data

The two regional inversions both used data from a ring of five

towers (Miles et al., 2012; denoted from here on as the ‘Ring’).

These five sites (Fig. 1) were located in the MCI region of the

NACP (Ogle et al., 2006) and were outfitted with Picarro

cavity ring down analyzers (Crosson, 2008). Hourly averages

were computed from mixing ratios of CO2 recorded every 2 s,

with daily calibrations. The analyzers had related measure-

ment errors that were approximately 0.2–0.3 ppm for the

hourly average mixing ratio data used in the two inversions

(Richardson et al., 2012). The towers were instrumented begin-

ning in May 2007. In addition to these data, both inversions

used calibrated CO2 data from the 40 m Missouri Ozarks

Ameriflux tower (Stephens et al., 2011) at the southern edge of

the domain as well as NOAA-ESRL data from the WLEF tall

tower in Wisconsin at the northern end of the domain and the

WBI tall tower in the center of the domain.

Inversions

Most trace gas inversions use the same basic principles and

structure that includes observations of trace gas concentra-

tions, a priori estimates for trace gas fluxes, a mapping from

fluxes to observations based upon an atmospheric transport

model and an optimization of trace gas fluxes to minimize

residuals between modeled trace gas concentrations and

observed trace gas concentrations. There is a rich literature on

the subject and several applications to CO2 fluxes (Tarantola,

1987; Enting et al., 1994; Evensen, 1994; Bishop et al., 2001;

Whitaker & Hamill, 2002; Tippett et al., 2003; Zupanski, 2005;

Peters et al., 2007; Lokupitiya et al., 2008). The goal of all three

inversions in this article, labeled as the Penn State University

(PSU) inversion, Colorado State University (CSU) inversion,

and CT inversion, is to provide time-varying mean and covari-

ance estimates for a set of spatial CO2 fluxes covering the MCI

region that are consistent with observed CO2 concentrations.

A simplified flowchart of the atmospheric inversion technique

is provided in Fig. 2 and the main differences among the three

inversion frameworks are summarized in Table 1. After

describing the domain for each inversion, a summary of

differences among the three frameworks is given with respect

to the following components (listed in Fig. 2): ‘Optimization’,

‘Atmospheric Transport’, ‘A priori CO2 fluxes’, ‘Boundary

Inflow CO2’, and ‘Observed CO2’.

Spatial domain and resolution. The PSU inversion was run

on a rectangular domain which overlapped portions of the

non-rectangular MCI domain. Consequently, estimates for the

PSU inversion were lacking for some areas in the MCI and

were provided for some areas not in the MCI. As a result, we

often present estimates for two areas, (i) the full MCI and (ii)

the intersection of the PSU inversion domain and the MCI,

which covers approximately 71% of the MCI domain. The

CSU domain consisted of most of North America and

extended out into the oceans to the east and west. Both

domains are shown in Figure A1. The CT domain is global.

The CSU inversion domain consisted of a grid of 200 km by

200 km gridcells over most of North America with higher

resolution grid of 40 km by 40 km grid cells over the MCI,

ROSEMONTROSEMONT

GALESVILLEGALESVILLEROUND ROUND LAKELAKE

WBIWBI

OZARKSOZARKS

CENTERVILLECENTERVILLEMEADMEAD

WLEFWLEF

KEWANEEKEWANEE

Fig. 1 Map of MCI domain located in north central United States.

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

1426 A. E. SCHUH et al.

covering the entire underlying transport grid. The PSU inver-

sion domain consisted of a grid of 20 km by 20 km gridcells

over their transport grid. Both can be seen in Figure A1. The

CSU and PSU inversion systems are grid based and allow flux

adjustments to each individual grid cell of their inversion

domain, relative to constraints imposed by a priori flux covari-

ances. The CT inversion grid consists of ecoregions as seen in

Figure A2. The CT system scales each individual ecoregion’s

net ecosystem exchange (NEE) up or down each week and

does not have the ability to provide any sub-ecoregion level

flux adjustments (i.e. all cells are adjusted in the same manner

within the region). The effect of the inversion resolution is

tightly coupled to the a priori covariance assumptions which

will be discussed later. It is important to note that due to the

sparseness of available CO2 observations, the resolution of the

inversion domain is coarser than that of the underlying trans-

port and a priori fluxes.

Optimization and temporal resolution. The CSU inversion

technique is a weekly sequential Bayesian batch inversion pro-

viding optimized total respiration (OPT_TRESP) and gross

primary production (OPT_GPP) on a weekly time scale at

40 km by 40 km over the MCI and 200 km continentally. A

priori total respiration (TRESP) and gross primary production

(GPP) are independently ‘corrected’ via regression factors,

bTRESP and bGPP applied to the a priori fluxes. The model and

associated cost function, F(x), for a particular week, or ‘cycle’

are as follows:

OPT TRESPðx; y; tÞ ¼ bTRESPðx; yÞTRESPðx; y; tÞ ð1Þ

OPT GPPðx; y; tÞ ¼ bGPPðx; yÞGPPðx; y; tÞ ð2Þ

OPT NEEðx; y; tÞ ¼ OPT RESPðx; y; tÞ �OPT GPPðx; y; tÞ ð3Þ

FðbÞ ¼ 1

2½ðb� b0ÞTB�1

b�b0ðb� b0Þ þ ðHðb � fluxpriorÞ

� obsÞTR�1ðHðb � fluxpriorÞ � obsÞ� ð4Þwhere B and R are the associated covariance matrices for the a

priori flux corrective factor errors and the model/data mis-

match, where b is the true but unknown correction factor on

the fluxes and b0 is the assumed correction factor, a priori. H is

the observation operator providing the mapping from the flux

space to concentration space and obs is the observed CO2

vector.

The PSU inversion technique is a weekly sequential

Bayesian batch inversion providing optimized estimates of

daytime NEE and nighttime NEE on a 7.5 day time scale at

20 km by 20 km spatial resolution. In contrast to optimizing

‘correction factors’ as the CSU inversion does, the PSU inver-

sion directly optimizes the fluxes. The associated cost function

is as follows:

Table 1 Comparison of inversion model components

CarbonTracker CSU (SiB-RAMS-LPDM) PSU (WRF-LPDM)

Inversion method Ensemble Kalman filter Synthesis Bayesian Synthesis Bayesian

Transport TM5 BRAMS 3.2* WRF-Chem

Land surface model† TESSEL SiB3-CROP NOAH

A priori CO2 fluxes/photosynthesis

model type

CASA (LUE) SiB3-CROP (Farquhar) SiB3-CROP (Farquhar)‡

Domain Global Continental (North America) Regional

Transport resolution 3 9 2deg (1 9 1 deg nest) 40 km 10 km

Inversion resolution Ecoregions (Olsen) 40 km/200 km nest§ 20 km

Boundary CO2 None (global) CarbonTracker and GlobalView Aircraft-corrected

CarbonTracker

*BRAMS 3.2 was used as the basis for the transport model but the code has undergone numerous changes, fixes, and improvements

over the last decade at Colorado State University.†The LSM used to drive the meteorology in the inversion, not necessary consistent with the LSM used to generate the a priori CO2

fluxes.‡CarbonTracker posterior CO2 fluxes were also used in Lauvaux et al. (2012a,b) but not shown here.§See notes in Inversions section.

Fig. 2 Flowchart of atmospheric inversion process.

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

PREDICTING CO2 FLUX OVER THE MIDWESTERN USA 1427

F ¼ 1

2½ðflux� fluxpriorÞTB�1

flux�fluxpriorðflux� fluxpriorÞ

þ ðHðfluxÞ � obsÞTR�1ðHðfluxÞ � obsÞ� ð5Þwhere B and R are the associated covariance matrices for the a

priori flux errors and the model/data mismatch. H is the

observation operator providing the mapping from the flux

space to concentration space and obs is the observed CO2 vec-

tor. We note that the PSU inversion was run from June

through December of 2007 due to its domain and dependency

on the Ring data which began in June 2007. Where annual

totals were required, a priori CO2 distributions were used. This

is not likely to be a critical limitation to the comparison, how-

ever, because the dominant fluxes are occurring between June

and August. In addition, the PSU inversion uses an a priori

annual flux consistent with the removal of harvested crops

and thus one would not expect large differences in the optimi-

zation during January through May, when respiration is the

primary CO2 flux.

The NOAA ‘CT system is based on a sequential ensemble

Kalman filter (EnKF) framework and provides optimization of

NEE from 2000 through 2009 on a weekly time scale at the res-

olution of ‘ecoregions’. The correction to NEE is performed

multiplicatively similar to the CSU inversion although the

complete procedure is more complicated (Supporting Infor-

mation, Appendix A2). Although the statistical procedure is

applied to ecoregions, the results are often presented as the

ecoregion correction factor applied to the higher resolution

underlying a priori flux field, which gives an artificial sense of

precision. We present mean results from CT in this fashion

but use fractional ecoregion-wide uncertainty for the variabil-

ity estimates.

Atmospheric transport. The WRF-Chem (Skamarock et al.,

2005) was used for transport by the PSU inversion system at a

resolution of 10 km by 10km. A CSU version of the Brazilian

Regional Atmospheric Modeling System (BRAMS) was used

for transport in the CSU model at a resolution of 40 km by

40 km (Pielke et al., 1992; Denning et al., 2003; Nicholls et al.,

2004; Wang et al., 2006; Corbin et al., 2010; Schuh et al., 2010).

Transport fields are provided for CT by the TM5 model (Krol

et al., 2005), and those winds are derived from the ECMWF

operational forecast model. Model resolution is 6° by 4° glob-ally with nests down to 1° by 1° over the United States. The

main difference here is that the regional models will be more

accurate at resolving synoptic scale transport, i.e. storms, and

vertical transport near the surface due to more highly resolved

vertical grids.

The Lagrangian particle model LPDM (Uliasz & Pielke,

1991; Uliasz, 1993, 1994, 1996) is used by both PSU and CSU. It

effectively acts as a transport adjoint (i.e. ‘inverse’) by diag-

nosing turbulent motions in the atmosphere as a function of

high time resolution fields of zonal and meridional winds,

potential temperature, and turbulent kinetic energy output

from a parent mesoscale model. This allows for the creation of

a Jacobian matrix representing the partial derivatives of CO2

concentration (at a fixed location) with respect to the sur-

rounding fluxes of CO2. The details of the Lagrangian model

that produces the particle movements from the parent

mesoscale model can be found in Uliasz (1994) and there are

many applications in the literature (Zupanski et al., 2007;

Lauvaux et al., 2008, 2012b; Schuh et al., 2009, 2010). Further

details on this technique can be seen in the Supporting Infor-

mation, Appendix D1.

A priori CO2 fluxes. The inversions use a priori CO2 flux dis-

tributions that are Gaussian in nature and are thus composed

of mean and covariance information.

Means: The a priori flux assumptions for the CSU and PSU

regional models are based on the Simple Biosphere model

(SiB), a land surface parameterization scheme originally used

to compute biophysical exchanges in climate models (Sellers

et al., 1986), but later adapted to include ecosystem metabo-

lism (Denning et al., 1996; Sellers et al., 1996). The photosyn-

thesis in SiB follows the Farquhar approach (Farquhar et al.,

1980). A phenology-based crop module was then added to SiB

and is detailed in Lokupitiya et al. (2009). This model was

used in two ways. First, hourly CO2 fluxes were calculated

from offline runs of the model driven by North American

Regional Reanalysis meteorological data, at 40 km by 40 km

resolution and 10 km by 10 km resolution, respectively, with

three sub-gridscale landcover patches for each configuration.

Secondly, the CSU model also ran test cases in which the

SiB-CROP model was run in coupled-mode inside of BRAMS

in an effort to provide consistency between the modeled CO2

fluxes and the meteorological data.

For CT, the a priori NEE estimates are recreated from

CASA-GFEDv2 model runs of the Carnegie-Ames Stanford

Approach (CASA) biogeochemical model, which employs a

light use efficiency (LUE) photosynthesis model based upon

AVHRR NDVI and year-specific weather. Global 0.5° by 0.5°resolution monthly output from the CASA-GFEDv2 model

(van der Werf et al., 2006) for GPP and TRESP is scaled down

to 3 hourly fluxes using a simple Q10 relationship and a linear

scaling for photosynthesis based upon ECMWF analyzed

meteorology. These are then differenced to provide diurnally

varying NEE, while conserving monthly mean NEE in a man-

ner similar to that of Olsen & Randerson (2004). The most

significant differences between the CT inversion and regional

inversions is the lack of an explicit crop model and the lack of

explicit sub-daily predictions of C exchange in CASA-

GFEDv2.

Covariances: For the CSU inversion, a priori covariance matri-

ces for the multiplicative biases on GPP and TRESP (b factor

in Eqn 4) were formed by constructing isotropic exponential

spatial covariance structures over North America with decor-

relation length scales of 500 and 1000 km (more information

available in the Supporting Information, Appendix A4) and

scaling them to 0.2, which amounts to standard deviations of

20% on GPP and TRESP. A priori covariance assumptions for

the PSU inversion, i.e. Bflux�fluxprior (see Eqn 5), included smaller

decorrelation length scales (exponential covariance) of approx-

imately 300 km, compared to the CSU inversion which gener-

ally employed 500 and 1000 km for results shown in this

article. The smaller decorrelation length scales of the PSU

inversion were further decreased by modeling the covariance

length scale as a function of ecosystem type, resulting in

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

1428 A. E. SCHUH et al.

equivalent isotropic decorrelation length scales of approxi-

mately 100 km. The temporal correlations were calculated

consistent with Lauvaux et al. (2009). More information on a

priori covariance of flux fields in the PSU inversion is available

in the Supporting Information, Appendix A4 and Lauvaux

et al. (2012b). There are no explicit spatial correlation assump-

tions in CT due to the use of larger ecoregions in its optimization

but the a priori standard deviations are 0.85 on each ecoregion,

amounting to a standard deviation of 85% of a prioriNEE.

The main difference in covariance structures between the

inversions is directly related to the ability of the inversions to

assign, or adjust the prior based on the observed CO2 concen-

trations, on a finer scale within the MCI region. The PSU

inversion has the most freedom to make fine scale adjustments

due to smaller spatial correlations followed by the CSU inver-

sion with a moderate ability to correct subregional fluxes. The

CT inversion is limited to multiplicative corrections on NEE

which are equally applied across the ecoregions (Figure A2)

and thus is the most restricted.

Boundary inflow CO2. While global inversion systems like

CT inherently have no boundaries, regional inversion results

can be very sensitive to boundary conditions, i.e. the inflow of

CO2 from the boundaries of the model domain (Goeckede

et al., 2010b; Gourdji et al., 2012). The CSU inversion benefits

from much lower variability in boundary inflow due to its

eastern and western boundaries being over the ocean. This

will make boundary bias corrections easier than correcting for

boundary inflow over locations with more variability in CO2

fluxes occurring in the middle of the continent (PSU).

However, the distance between the boundaries of the

domain and the boundaries of the MCI make the CSU inver-

sion dependent upon optimized fluxes over the continent with

much weaker observational constraints. In particular, the CSU

inversion utilizes inflow estimates (optimized CO2) from the

global CT inversion system with a bias correction based on

interpolated global CO2 from NOAAs GlobalView (GV) prod-

uct while the PSU inversion also utilizes optimized CT CO2

bias corrected with routine NOAA aircraft flights near their

domain boundaries (Lauvaux et al., 2012b). We provide results

with both bias-corrected and uncorrected CT inflow for the

CSU inversion and detail the bias correction procedure in the

Supporting Information, Appendix A3.

Observed CO2. The PSU and CSU inversions both used the

Ring data while using slightly different data streams from

NOAA tall towers at WLEF in Wisconsiin and WBI in Iowa.

The PSU inversion used data from 122 m at WLEF and 99 m

at WBI meters to be consistent with the other tower heights

while the CSU inversion used the highest levels for WLEF and

WBI which are 396 and 379 m, respectively. The full observa-

tional constraints for the PSU and CSU inversions are summa-

rized in Table 2. As mentioned earlier, the PSU inversion only

ran from June through December. The CSU and CT inversions

used data from the NOAA WLEF and WBI tall towers from

January to May and otherwise were constrained by the sparser

continental network. The effect of the data gap on the PSU

inversion is probably minimal in this study because of the a

priori knowledge that a large percentage of the Net Primary

Production is removed from the study region and not avail-

able for decomposition, however, we emphasize that, in gen-

eral, this should not be the case.

The CT inversion is nearly real-time operational and uses

global in situ as well as flask-collected data in its flux optimi-

zation (Peters et al., 2007). An important note is that it does

not use the Ring data situated in the heart of the MCI region

(Miles et al., 2012). Modified runs were performed with the

data from the Ring for 2008. However, the inclusion of the

data did not significantly alter the cropland flux estimates,

instead increasing uptake in upwind grassland/shrub areas

to the west and no additional diagnosis was performed to

determine the exact cause of the insensitivity of local fluxes to

the Ring data. Therefore, the original and publicly available

flux estimates (CarbonTracker, 2009) were used in this study.

The lack of any sensitivity of CT to the Ring data, and inabil-

ity to optimize subregional fluxes, were two particular rea-

sons that mesoscale inversions were employed in this study.

Specified model-data mismatch errors (the R matrix in

Eqns 4 and 5) correspond to posterior model fits of the observa-

tions and thus, theoretically, are generally not available before

the inversion step is run. The errors in the CSU inversion are

thus formed by running the inversion initially using differ-

ences between the a priorimodeled CO2 concentrations and the

observations and then reducing this a priori error by a some-

what arbitrary 40%. To create the model-data mismatch in the

PSU inversion, R, the framework used a combination of projec-

tions of boundary layer depth errors and forward-adjoint con-

sistency to create the errors. The CT system uses subjective

choices for the errors which depend upon the location of the

observing tower and how well the authors felt that the trans-

port model, TM5, could reproduce local atmospheric motions

there (see Supplementary Material, Peters et al., 2007). All three

inversions calculate the chi-square innovation statistic and use

this value to scale the a priori model-data mismatch to guaran-

tee that they do not overestimate or underestimate the model-

data mismatch a priori, which reduces some of the apparent

dependency on the initial setting of R described above.

Inventory methods

A bottom-up CO2 flux inventory was compiled for the MCI

region for evaluating against the atmospheric inversion

results. This inventory utilizes data on forest biomass, har-

vested woody products, and agricultural soil C from the US

Greenhouse Gas Inventory (EPA, 2010; Ogle et al., 2010), in

addition to fine resolution data on fossil and biofuel CO2 emis-

sions (Gurney et al., 2009), CO2 uptake by agricultural crops

and grain harvest (West et al., 2011), and CO2 losses through

livestock and human respiration associated with agricultural

products (West et al., 2011). Uncertainties were derived from a

Monte Carlo analysis in which probability distribution func-

tions were developed for the flux estimates from each of the

sources and random draws were made to produce 100 realiza-

tions of the total flux in the region. The carbon inventory was

constructed on an annual time frame, due to temporal limita-

tions in the FIA and harvest statistics, and was derived from

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

PREDICTING CO2 FLUX OVER THE MIDWESTERN USA 1429

spatial data with a US county level resolution. For example,

US counties in Iowa are very homogenous in size and shape

and have a resolution of approximately 40 km by 40 km and

thus the county sizes are comparable to the 0.5° by 0.5° resolu-tion grid cells used to display the inventory.

Results

Bottom-up annual inventory of CO2 fluxes

Based on the bottom-up inventory analysis, sources of

CO2 in the MCI domain are dominated by fossil fuel

combustion (262 TgC source), in particular the city of

Chicago (Gurney et al., 2009). Inversions usually

consider fossil fuel fluxes as ‘known’ and without error

and optimize the nonfossil fuel CO2 fluxes due to better

knowledge of fossil fuel combustion when compared to

natural biospheric fluxes and difficulties optimizing

very localized point sources of CO2. The nonfossil fuel

inventory data show a net CO2 uptake of 135 TgC for

2007 and are shown in Fig. 3. The flux is dominated by

the harvest and export of grain from the region (West

et al., 2011). Smaller sources and sinks associated with

feedlots, forests, other natural vegetation, and human

respiration also contribute to the total. Uncertainty for

the nonfossil inventory is largely dominated by the har-

vest product while relative uncertainties, i.e. standard

deviation in NEE as function of mean NEE, is largest

for the FIA forest product. The spatial correlations in

the inventory impact the region-wide uncertainty and

can be better understood by an investigation of Fig. 3

of Cooley et al. (2012). Using a Monte Carlo analysis

based on uncertainties in each component flux, we con-

structed 95% confidence limits on the CO2-C balance

(net fossil fuels) of the MCI domain which resulted in a

sink of �104 to �204 TgC for 2007 (mean: �135 TgC).

Annual CO2 fluxes from inversions

The results for all three inversions are statistically indis-

tinguishable from the inventory results for the annual

Table 2 CO2 observations

Site Height Contact PSU inversion CSU inversion

CarbonTracker

inversion

Argyle, ME 107 m A. Andrews, NOAA-ESRL Outside domain 12:00–18:00 LST 12:00–16:00 LST

Centerville, IA 110 m N. Miles/S. Richardson,

Penn State U

All hours 12:00–18:00 LST Not used

Candle Lake, BC 30 m D. Worthy, EnviroCanada Outside domain 12:00–18:00 LST 12:00–16:00 LST

Fraserdale, ON 40 m D. Worthy, EnviroCanada Outside domain 12:00–18:00 LST 12:00–16:00 LST

Galesville, WI 122 m N. Miles/S. Richardson,

Penn State U

All hours 12:00–18:00 LST Not used

Kewanee, IL 140 m N. Miles/S. Richardson,

Penn State U

All hours 12:00–18:00 LST Not used

Park Falls, WI 122 m/396 m A. Andrews, NOAA-ESRL All hours (122 m) 12:00–18:00 LST (396 m) 12:00–16:00 LST

(396 m)

Lac Labiche, AB 10 m D. Worthy, EnviroCanada Outside domain 12:00–18:00 LST 12:00–16:00 LST

Metolius, OR 33 m M. Goeckede/Beverly Law,

Oregon State University

Outside domain 12:00–18:00 LST Not used

Mead, NE 122 m N. Miles/S. Richardson,

Penn State U

All hours 12:00–18:00 LST Not used

Missouri

Ozarks, MO

30 m N. Miles/S. Richardson,

Penn State U

All hours 12:00–18:00 LST Not used

Round Lake, MN 110 m N. Miles/S. Richardson,

Penn State U.

All hours 12:00–18:00 LST Not used

Sable Island, NS 25 m D. Worthy, EnviroCanada Outside domain 12:00–18:00 LST 12:00–16:00 LST

West Branch, IA 99 m/379 m A. Andrews, NOAA-ESRL All hours (99 m) 12:00–18:00 LST (379 m) 12:00–16:00 LST

(379 m)

Moody, TX 457 m A. Andrews, NOAA-ESRL Outside domain 12:00–18:00 LST 12:00–16:00 LST

Observations used by inversions. All towers used by PSU inversion were used by CSU inversion. Additional towers were used by

CSU due to larger domain size. CarbonTracker use of data, common to PSU and CSU inversions, is shown as ancillary information.

CarbonTracker is a global inversion framework and thus makes use of large amounts of data outside of North America which are

not detailed here. Although custom filtering of observations is inversion dependent as well as dependent upon quality flags/opera-

tibility of the towers, the times for considered data in each inversion are given in the table. PSU inversion uses all hours

but with different weightings for different times of day and therefore nocturnally collected data is usually weighted more weakly,

see Lauvaux et al. (2012b).

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

1430 A. E. SCHUH et al.

net CO2 budget of the region (Fig. 4). After correcting

the regional inversions for boundary inflow, all three

inversion estimates show a slightly stronger sink than

the inventory (CT = �155 � 173 TgC, PSU = �140 � 26

TgC for reduced ‘PSU domain’, CSU = �145 � 29 TgC).

The difference in the inversion system results was

primarily influenced by the a priori flux uncertainty

estimates, i.e. the initial range for the ‘best guess’ NEE.

The CSU inversion used independent �20% standard

deviations for GPP and TRESP fluxes which is equiva-

lent to an enormous range of possible flux results. The

particular choice of 20% comes from the desire to keep

correction factors positive, ensuring positive optimized

GPP and TRESP. These conservative choices introduce

flux scenarios that could be well outside the range of

reasonableness, for example a 20% increase in annual

TRESP and 20% reduction in annual GPP, relative to a

balanced biosphere would cause a C source on the

order of 300 TgC. It is important to note that the vari-

ability around the CT estimate is unrealistically large.

This is well known and documented (CarbonTracker,

2011). However, the predictions generally appear more

accurate than would be inferred from the formal flux

uncertainty.

The three inversions produce similar spatial patterns

in annual NEE compared to the inventory, with an

important sink in the center of the domain correspond-

ing roughly to the highest density of agricultural area

(Fig. 5). However, at finer scales, the location of the

maximum of uptake and the shape of the sink area var-

ies substantially among the inversions. To evaluate this

pattern, the inversion results were compared to the

inventory data from the individual grid cells. Scatter-

plots of annual NEE values for the inversions vs. the

inventory are shown in Fig. 6. Correlations with the

inventory are higher for the CSU (r = 0.76) and PSU

(r = 0.55) inversion results. The weaker correlation of

the CT results with the inventory (r = 0.36) can be seen

along with a bimodal feature in the figure.

Much of the spatial structure in the estimated maps

of net annual flux is driven by the structure of the

Bayesian a priori mean and the optimization method in

each inversion model, i.e. the degree to which the

inversion framework allows for independent adjust-

ments to the a priori fluxes given the observed CO2

data. The CSU inversion shows a strong correlation

with the a priori June/July/August uptake in the

region, but with a weaker C sink in Illinois and a stron-

ger C sink in western Iowa. The spatial resemblance to

the inventory is likely due to the strong 500–1000 km a

priori decorrelation lengths used in the inversion and

the strong summer time CO2 deficit. Using a 500-km

decorrelation length as an example, and noting that the

width of Iowa is about 500 km, the inversion would

assume that a weekly multiplicative error in GPP on

one end of Iowa is correlated with an error in GPP on

the other end of Iowa at a level of 0.37, a priori. Posterior

correlations were reduced by about half although the

reduction was different for GPP and TRESP and not

isotropic, instead following the sampling gradient.

There were no significant differences between using

500 and 1000 km on the regional NEE (Table 3).

The smaller a priori decorrelation length scales used

in the PSU inversion, approximately five times less that

those used in the CSU inversion, lead to much finer

spatial adjustments in the a priori fluxes within the

region. The PSU inversion shows a very large sink in

the eastern part of the domain (northern Illinois),

20–30% larger than the inventory estimate in the area,

as well as a stronger more diffuse sink to the northeast

of the domain, an area of larger uncertainty in the

inventory.

In contrast, the strongest sink for the CT inversion is

located in the extreme northwest portion of the MCI

Inventory 2007 annual NEE mean (GgC per 0.5°x 0.5°)

LON

LAT

38

40

42

44

46

48

−100 −95 −90 −85

−800

−600

−400

−200

0

200

Inventory 2007 annual NEE S.D. (GgC per 0.5°x 0.5°)

LON

LAT

38

40

42

44

46

48

−100 −95 −90 −850

100

200

300

400

500

Fig. 3 Annual NEE estimate by the inventory components. Mean estimates are shown in left panel and standard deviations are shown

on right side. Note that the distribution of the inventory is not necessarily Gaussian and therefore, in a rigorous sense, the standard

deviation is simply a measure of uncertainty.

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

PREDICTING CO2 FLUX OVER THE MIDWESTERN USA 1431

although the overall sink appears more diffuse. This is

likely due to a strong flux in the prior for this particular

area of the MCI and may be a result of inadequate crop

modeling in CASA, which does not explicitly account

for agricultural crops. Northern portions of the MCI

have strong influences from soybeans and spring

wheat, but these crops do not assimilate as much car-

bon during the peak of summer according to the inven-

tory and eddy covariance studies (Lokupitiya et al.,

2009), suggesting that a mix of wheat and soybeans

contributes a weaker NEE signal than a mix of

soybeans and corn. Overestimating the flux in the

northwest portion of the MCI led to the bimodal distri-

bution in flux mismatch between the CT inversion and

inventory that was apparent in Fig. 6.

Although not included in Fig. 4, we also assessed the

variability in CO2 inflow and its effect on the PSU and

CSU inversions. For the CSU inversion, this sensitivity

can be viewed in Table 3 while a general discussion of

the inflow uncertainty for both regional inversions is

provided later.

Transport and boundary inflow considerations

The transport and inflow boundary conditions could

also influence the pattern and strength of fluxes within

the region. However, the transport fields produced

from the mesoscale models displayed a surprising

amount of similarity. Despite different mesoscale mod-

els, PBL schemes, land surface models, and external

forcing scales in time and space, differences in time-

space integrated afternoon observation footprints for

the towers in the aaa‘ring’ remained on the order of

20% of the absolute signal or less, varying as a function

of distance from the tower (Supporting Information,

Appendix D). Among the differences between the

transport fields that could not be immediately

explained, was the sensitivity to surface fluxes as a

function of distance from tower. The RAMS model

(CSU) appeared to show weaker sensitivity in the local

vicinity of the tower and a stronger long-distance sensi-

tivity than the corresponding WRF model (PSU).

In addition, regional inversion results can be sensitive

to boundary conditions, i.e. the inflow of CO2 at the

boundaries (Goeckede et al., 2010b; Gourdji et al., 2012).

We evaluated the influence of inflow boundary condi-

tions on the CSU inversion by using the CT-optimized

CO2 as inflow with and without corrections for a known

Northern Hemispheric seasonal bias. Bias correction to

the CT optimized CO2 inflow reduced the CSU sink in

the MCI by approximately 33%, from 174 TgC to 117

TgC in the ‘online’ case, while reducing the continental

sink (data not shown) by 62% (1.6–0.6 PgC) providing

better agreement with independent CO2 inventory

estimates for North America (King et al., 2007). This

inflow sensitivity is consistent with the findings of

others who used similar methodologies (Gourdji et al.,

2012). Furthermore, this adjustment to boundary inflow

in the CSU inversion appeared, to first order, to simply

shift the posterior annual NEE up or down. Similar

results are summarized for the PSU inversion in the

Supporting Information (Appendix A3) and Lauvaux

et al. (2012b).

−250 −200 −150 −100 −500.00

00.

005

0.01

00.

015

0.02

00.

025

PSU domain

MCI: annual NEE 2007 (TgC)

Pro

babi

lity

dens

ity

−250 −200 −150 −100 −500.00

00.

005

0.01

00.

015

0.02

0

MCI domain

MCI: annual NEE 2007 (TgC)

Pro

babi

lity

dens

ity

CSUPSUCarbontrackerInventory

CSUCarbontrackerInventory

Fig. 4 Densities for annual NEE for inversion results and inven-

tory (2007). Top panel shows results for the intersection of the

PSU inversion model domain and MCI domain while bottom

panel shows results for the entire MCI region. PSU inversion is

based on SiB3-CROP offline prior. CSU inversion is also based

on SiB3-CROP offline prior with GV-bias-corrected CT inflow.

These results include explicit variability estimates that were

constructed for the inventory using a Monte Carlo anlysis and

variability estimates that arise naturally from the matrix-based

atmospheric inversion procedure. CarbonTracker variability

was approximated by summing fractional ecoregion-wide vari-

ability for each ecoregion which occurred in the MCI. Variability

estimates were unrealistically large and thus no effort was made

to include the whole pdf in the image. The CT mean is indicated

by a filled square. The variability induced by varying inflow

CO2 or underlying transport model characteristics is not implic-

itly included here but can be seen in Table 3.

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

1432 A. E. SCHUH et al.

We conducted an additional test by evaluating the

CSU inversion results outside of the MCI for consis-

tency with the bias-corrected inflow used by the PSU

inversion. Inflow estimates for the Kewanee tower were

calculated from the CSU inversion by subtracting out

the effect of the PSU inversion region from the CSU

modeled Kewanee CO2. In this fashion, we were able to

compare the expected inflow at the Kewanee tower

from the boundaries of the PSU inversion region, for

both the CSU and PSU inversion systems. Posterior

inflow estimates for the CSU inversion at the boundary

had a correlation of 0.82 compared to 0.41 for the a

38

40

42

44

46

48

−100 −95 −90 −85

PSU posterior − INVT

−100 −95 −90 −85

CSU posterior − INVT

−100 −95 −90 −85

CT posterior − INVT

38

40

42

44

46

48

PSU posterior CSU posterior CT posterior

38

40

42

44

46

48

PSU prior CSU prior CT prior

−800

−600

−400

−200

0

200

400

2007 Comparison of inversion results for NEE (GgC per 0.5°x 0.5° grid cell)

38

40

42

44

46

48

PSU prior JJA CSU prior JJA CT prior JJA

−1500

−1000

−500

0

Fig. 5 Each panel name is composed of the following(i) inversion model, (ii) 2007 for annual total or JJA2007 for June/July/August

sum, and (iii) ‘pr’ for a priori and ‘post’ for posterior flux. A priori annual 2007 NEE estimates are shown in middle row with posterior

annual 2007 NEE estimates shown in the bottom row. The bottom row consists of differences between the inversion models and the

inventory (INVT). PSU inversion is based on SiB3-CROP offline prior with residual 109 TgC harvest sink. CSU inversion is also based

on same prior (and underlying seasonality), but with residual harvest sink balanced by respiration annually to induce net zero NEE

and uses GlobalView bias-corrected CT inflow. The top row shows the June/July/August total NEE for each prior flux which is indica-

tive of the spatial signal of strong summer crop carbon drawdown. A few grid cell values were truncated at the bounds of the color bar

for visualization purposes. Multiplying fluxes by 0.45 gives approximate conversion into grams per square meter.

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

PREDICTING CO2 FLUX OVER THE MIDWESTERN USA 1433

priori inflow estimates and the mean difference between

the CSU inflow estimate and the PSU bias-corrected

inflow estimate dropped from 2.8 to 1.8 ppm. Thus,

despite limited towers outside of the MCI, the CSU

inversion appeared to provide inflow estimates at the

MCI boundary which were more consistent with the

bias-corrected CT inflow. However, a positive annual

difference exists in the inflows, 1.8 ppm. If this differ-

ence is allocated to the PBL, roughly 1/7 of the atmo-

spheric column, and spread evenly over the MCI

region, it appears to provide an explanation for the fact

that the CSU CO2 sinks are often 10–15% stronger than

the PSU CO2 sinks (Table 3).

Discussion

Continental and meso-scale inversions were developed

for 2007 using a relatively high density of observations

in the MCI region. These data were compared to a bot-

tom-up inventory and a global inversion framework,

CT, which did not assimilate the higher density of CO2

observations in the region. NEE flux estimates are simi-

lar among inversions, even from the CT system, and

are reasonable for 2007 in the sense that they are statis-

tically consistent with the inventory. These results are

promising because they show that CO2 inversion meth-

ods can be robust, in the sense that they deliver similar

inverse flux solutions which are consistent with C

inventory results, despite being constructed across very

different frameworks, e.g. global to continental to regio-

nal, with very different assumptions. Nevertheless,

comparisons to the inventory at spatial scales finer than

100–200 km and finer temporal scales on the order of

weeks (data not shown), demonstrate the value of

higher resolution inversion systems that can benefit

from finer scale observations in terms of recovering

finer CO2 flux patterns within a region.

The agreement of large-scale posterior CT CO2 fluxes

to the inventory, despite major differences in fine scale

flux signals may be fortuitous. The minimum scale of

the gradients of CO2 resolved by the CT transport

model TM5 at 1° by 1° resolution is likely in the

200–300 km range. However, the region was chosen to

avoid complex meteorology induced by land-sea

contrasts or complicated topography. Hence, if the

observations used by CT constrain the MCI domain

reasonably well, it is certainly reasonable to recover

large-scale agreement in flux estimates. Nevertheless,

the very nature of the coarse inversion region used by

CT (Supporting Information, Appendix A1) prohibits

the CT system from recovering fluxes on most scales

less than the MCI region and forces strong coherence to

a priori CASA flux patterns at higher resolutions. Fur-

thermore, the lack of higher resolution attribution of

flux errors might limit this type of inversion from being

used to further future prognostic carbon cycle model-

ing efforts.

The PSU inversion framework uses the most highly

constrained area, i.e. an area slightly larger than the

Ring of towers. The advantages of this are that they use

a wealth of eddy covariance tower data to help con-

strain the a priori fluxes as well as provide more flexibil-

ity spatially to adjust fluxes. This was shown in

Lauvaux et al. (2012b) to allow some degree of robust-

ness of the posterior flux result to distinct underlying a

priori flux fields. Therefore, given dense enough obser-

vational coverage of CO2, one would expect to be able

to proceed toward improvements in prognostic carbon

cycle modeling where this is not possible with the CT

inversion system. The disadvantage of this particular

inversion is that the corrections to inflow on the sides of

the domain will likely be larger and more variable than

those made over marine boundary layer conditions and

require the use of aircraft to obtain vertical profiles.

−0.8 −0.6 −0.4 −0.2 0.0 0.2

−0.

8−

0.4

0.0

0.2

CSU (w/GV−corrected CT inflow)

Inventory (TgC/yr)

Inve

rsio

n (T

gC/y

r)

r = 0.75Bias = 0.02 TgC

−0.8 −0.6 −0.4 −0.2 0.0 0.2

−0.

8−

0.4

0.0

0.2

Carbontracker

Inventory (TgC/yr)

Inve

rsio

n (T

gC/y

r)

r = 0.36 Bias = 0.05 TgC

−0.8 −0.6 −0.4 −0.2 0.0 0.2

−0.

8−

0.4

0.0

0.2

PSU (w/CT inflow correction)

Inventory (TgC/yr)

Inve

rsio

n (T

gC/y

r)

r = 0.55 Bias = 0.04 TgC

Fig. 6 Plots of inventory estimates vs. inversion for annual 2007 NEE. Each pixel of Fig. 4 is represented as a datum in the figure. PSU

inversion is based on SiB3-CROP offline prior. CSU inversion is also based on SiB3-CROP offline prior with GV-bias-corrected CT

inflow.

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

1434 A. E. SCHUH et al.

Table

3MCIsource/

sinkresu

lts(dueto

model

variations)

Inversion

method

Inflow

Priordescription

PriorNEE

(MCI)

Post

NEE

(MCI)

PriorNEE

(PSU

Dom.)

Post

NEE

(PSU

Dom.)

PriorNEE

(PSU

Dom.)

(June–Decem

ber)

Post

NEE

(PSU

Dom.)

(June–Decem

ber)

CarbonTracker

N/A

CASA-G

FED

�40TgC

�155

TgC

�30TgC

�125

TgC

�124

TgC

�196

TgC

PSU

Aircraft-correctedCT

SiB3-offline

N/A

N/A

�65TgC

�140

TgC

�109

TgC

�185

TgC

PSU

Aircraft-correctedCT

CarbonTracker

optimized

N/A

N/A

�154

TgC

�127

TgC

CSU

CarbonTracker

opt.

SiB3-offline

�82TgC

�235

TgC

�75TgC

�200

TgC

�126

TgC

�251

TgC

CSU

GV-correctedCTopt.

SiB3-offline(forced

annual

balan

ce)

0TgC

�145

TgC

�75TgC

�127

TgC

�66TgC

�203

TgC

CSU

GV-correctedCTopt.

SiB3-offline(dec

length:10

00km)

�82TgC

�162

TgC

�75TgC

�144

TgC

�127

TgC

�213

TgC

CSU

GV-correctedCTopt.

SiB3-offline(dec

length:50

0km)

�82TgC

�160

TgC

�75TgC

�143

TgC

�127

TgC

�213

TgC

CSU

CarbonTracker

opt.

SiB3-RAMScoupled

0TgC

�174

TgC

0TgC

�154

TgC

�62TgC

�208

TgC

CSU

GV-correctedCTopt.

SiB3-RAMScoupled

0TgC

�117

TgC

0TgC

�107

TgC

�62TgC

�177

TgC

Inven

tory

�135

TgC

�117

TgC

Neg

ativeNEEindicates

carbonmovingfrom

atmosp

hereto

thebiosp

here.TheseSiB3-offlinefluxes

weredriven

from

offlinerunofthemodel

driven

byNARRdata,

whichwere

usedas

thedrivingexternal

forcingnecessary

forboth

WRFan

dRAMS.Inversionresu

ltsforPSU

inversionareputonafullan

nual

2007

basis

byad

dingapriorifluxes

from

SiB3-CROPforJanuary–M

ay20

07(before

MCItowerswereinstrumen

ted)to

both

apriorian

daposteriorfluxestimates

forJune20

07throughDecem

ber

2007

.PSU

inversion

resu

ltsforthe‘optimized

CarbonTracker

flux’case

areonthenativePSU

gridwhichisslightlylarger

than

the‘PSU

grid’whichisusedthroughoutthisarticlewhichrepresents

theintersectionofthenativePSU

gridan

dtheMCIdomain.A

priori

fluxes

from

SiB3-offlinearech

aracterized

bya‘realistic’an

nual

harvestsinkwhilethe‘forced

annual

balan

ce’case

forces

NEEto

zero

over

allgridcellsbybalan

cingtotalresp

irationwithgross

primaryproduction.T

ypically,theapriorifluxes

andtran

sportarederived

inadecou-

pleden

vironmen

t.Howev

er,the‘SiB3-RAMS’apriorifluxes

arethose

producedas

aresu

ltoftheparen

tSiB3-RAMSsimulation,whichproducedthetran

sport

usedin

theCSU

inversion,i.e.

coupled.‘D

eclength’indicates

theapriori

decorrelation

length

scale,

ore-foldinglength,used

fortheexponen

tial

spatialcorrelation

intheapriori

fluxes.

Thisvalueisgen

erally

less

than

300km

forPSU

inversionsan

d10

00km

forCSU,unless

otherwisenoted.

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

PREDICTING CO2 FLUX OVER THE MIDWESTERN USA 1435

The CSU inversion is largely a compromise between

the CT and PSU systems. Boundary inflow corrections

are still necessary because of the regional nature of the

inversion but are made over marine boundary sites that

are generally less variable in time and space and

observed with the operational NOAA flask network.

This tends to preserve the a priori flux gradients around

the perimeter of the MCI because rapid flux adjust-

ments are not needed to force agreement between

tower observations and model observations close to the

model domain boundary. The disadvantage is the need

for a unified framework to simultaneously model the

more densely observed MCI region and the rest of the

continent. This topic was studied recently (Wu et al.,

2011), but the heterogenous nature of the evolving CO2

observing network probably demands continued inves-

tigation especially as satellite observations of CO2

become available. Furthermore, the impact of estimat-

ing (i) NEE, (ii) day/night NEE, or (iii) total respiration

and GPP upon the inversions is still uncertain and

remains an active research question.

With respect to our secondary objectives, differences

between the inversions and inventory were influenced

by boundary inflow estimates of CO2, a priori flux sig-

nals and differences in transport. As can be clearly seen

from Table 3, the domain wide flux is most strongly

influenced by the inflow estimates. Finer spatial scale

flux variations then result from differences in transport

and a priori flux patterns. Increased observations in the

inversion domain should lessen the impact of the a

priori flux assumptions, but the inflow estimate errors

generally remain a systematic error, which must be cor-

rected in an independent manner. Inflow corrections

were performed using the GV NOAA product and

the NOAA weekly aircraft samples as the basis of

the bias correction scheme to the optimized global

CT CO2 product and significantly improved the

accuracy of the inversion results we showed. This dem-

onstrates the importance of maintaining well calibrated

global CO2 networks and in particular aircraft profile

programs with respect to estimating regional carbon

budgets with CO2 data. Differences in the bias-

corrected inflow estimates between the two regional

inversion appeared to be the primary cause of the

differences in the annual CO2 flux estimates from the

MCI region as a whole.

Posterior variance estimates of CO2 exchange con-

tinue to be one of the most difficult estimates to make

for inversion modelers. Variance estimates from these

CO2 inversion systems are sensitive to both inversion

method and a priori covariance specifications. For

example, posterior covariance from EnKF methods

such as used for CT are strongly dependent upon the

particular EnKF algorithm (Tippett et al., 2003). The a

priori flux variances are generally very conservative on

annual scales. Standard deviations of 85% on ecore-

gion-wide NEE for CT and standard deviations (inde-

pendent) of 20% for TRESP and GPP for the CSU

inversion led to a large range of possible net fluxes; far

stronger annual sources and sinks than could be possi-

ble given global constraints and thus sufficiently con-

servative. Shortages of ancillary information on NEE,

such as spatially dense eddy covariance observations or

temporally and spatially rich biomass accumulation

statistics often necessitate ‘broad’ a priori covariance

structures be used in inversion systems attempting to

estimate fluxes over continental or larger regions. While

inversion modelers can attempt to control for portions

of this uncertainty, i.e. model methodology, other por-

tions such as ancillary data to constrain the fluxes a

priori are generally outside of their control. Neverthe-

less, results from this study showed that quite good

agreement can result from two inversions (CSU and

PSU) where different a priori flux uncertainties, as well

as system and method, were used.

In summary, regional flux estimates from each of the

three frameworks agreed well with the estimates pro-

vided by the inventory data, but the continental and

meso-scale inversions were better able to recover the

spatial pattern of fluxes in the region. We consider this

a first step toward ascertaining feasibility of the CO2

inversion method to produce regional carbon flux

estimates as would be done under a monitoring pro-

gram. Moreover, this study shows that atmospheric

inversions are capable of capturing regional CO2 flux

estimates at sub-national scales, scales which will be

useful for future carbon-cycle research and regional

greenhouse gas initiatives. The most critical next steps

are to further refine the inversion frameworks to better

quantify boundary inflow uncertainty, sensitivity to a

prior flux estimates, and to provide explicit character-

izations of transport variability as well as leverage

the most recent and comprehensive sources of data

on CO2.

Author Contributions and Acknowledgements

Andrew Schuh and Thomas Lauvaux performed the biosphericmodel runs, atmospheric transport runs, and new atmosphericinversions included in this manuscript. Tristram West andStephen Ogle provided most of the inventory data used for the‘bottom up’ portion of the comparison with the exception of fos-sil fuel inventory data for the MCI region, which was providedby Kevin Gurney (Arizona State) and FIA data provided byLinda Heath and James Smith (US Forest Service). NatashaMiles and Scott Richardson instrumented, maintained andanalyzed the PSU ‘Ring of towers’ CO2 data for the MCI cam-paign (and the Missouri Ozarks tower) while Arlyn Andrewsdid the same for the WBI and WLEF towers within the MCIdomain, in addition to the remainder of NOAA’s tall tower sites

© 2013 Blackwell Publishing Ltd, Global Change Biology, 19, 1424–1439

1436 A. E. SCHUH et al.

across the US. Marek Uliasz provided assistance with the LPDMmodel used by both the PSU and CSU inversions. Dan Cooleyprovided advice and discussion on inversions and state-spacemodeling. Scott Denning provided the majority of the introduc-tion including the historical context. Ken Davis and StephenOgle helped initiate the original campaign, provided many use-ful comments on manuscript and provided overall guidance tothe project. The authors would like to thank a great many peo-ple who were involved with this project as well as generoussupport from the National Aeronautics and Space Administra-tion (NASA #NNX08AK08G), National Oceanic and Atmo-spheric Administration (NOAA #NA08OAR4320893) and theDepartment of Energy (DOE #DE-FG02-06ER64317). Thanks toNOAA-ESRL and Andy Jacobson in particular, for many usefuldiscussions on these inversions as well as the CarbonTrackerresults which were used in this paper. Tower data weregraciously provided, and commented on, by Beverly Law andMatthias Goeckede (Oregon State University), NOAA-ESRL(Arlyn Andrews), and Environment Canada (Doug Worthy).This research used the Evergreen computing cluster at thePacific Northwest National Laboratory. Evergreen is supportedby the Office of Science of the US Department of Energy underContract No. (DE-AC05-76RL01830).

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Supporting Information

Additional Supporting Information may be found in the online version of this article:

Data S1. Appendices.Figure A1. Inversion domains shown in native polar stereographic projections. Left panel (A) shows nested inversion grid withcoarser grid at 200 km by 200 km and fine grid over MCI at 40 km by 40 km. Right panel (B) shows high resolution 20 km by20 km grid for PSU inversion system.Figure A2. CarbonTracker ecoregion-based inversion domain. Figure courtesy of NOAA-ESRL.Figure C1. Time series of net ecosystem exchange (NEE) estimates from a variety of inversion models for 2007. PSU inversion isbased on SiB3-CROP offline prior. CSU inversion is also based on SiB3-CROP offline prior with GV-bias corrected-CT inflow.Results from PSU inversion are from the intersection of PSU inversion domain and MCI domain while the results for the Carbon-Tracker and CSU inversions are on the MCI domain.Figure D1. Sensitivity of daytime observations of passive surface flux to daytime passive flux releases during June, July, andAugust. Left panel shows results for PSU transport with WRF and LPDM and middle panel shows results for CSU transportwith RAMS and LPDM. Right panel shows the difference. Releases were constant 1 lmol C m�2 s�1 over the PSU inversiondomain (subset of MCI) and passive signal was integrated over this same area for both models.Figure D2. Sensitivity of daytime observations of passive surface flux to nighttime passive flux releases during June, July, andAugust. Left panel shows results for PSU transport with WRF and LPDM and middle panel shows results for CSU transportwith RAMS and LPDM. Right panel shows the difference. Releases were constant 1 lmol C m�2 s�1 over the PSU inversiondomain (subset of MCI) and passive signal was integrated over this same area for both models.

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